De Sitter Holography: Fluctuations, Anomalous Symmetry, and Wormholes

TL;DR

De Sitter Holography investigates whether holography can be meaningfully extended to de Sitter space by focusing on static patches and horizon-bound degrees of freedom. It proposes a static-patch holographic framework and a four-step symmetry protocol, then argues that finite entropy enforces a nonperturbative breaking of the de Sitter $O(d,1)$ symmetry via a Goheer–Kleban–Susskind anomaly, Boltzmann fluctuations, and higher-genus wormhole effects exemplified by the Nariai geometry. These results suggest that eternal de Sitter space may be best understood as an ensemble average rather than a single, perfectly symmetric microstate, with nonperturbative effects scaling as $e^{-S_0}$ and horizon entropy $S_0=rac{ ext{area}}{4G}$. The analysis is supported by a toy model, JT/SYK analogies, and GR-based fluctuation calculations, highlighting the deep connection between discreteness of the energy spectrum and nonperturbative gravitational phenomena in de Sitter holography.

Abstract

The Goheer-Kleban-Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in the light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests: the classical symmetry between different static patches is broken; and that eternal de Sitter space -- if it exists at all -- is an ensemble average.

Figures (17)

• Figure 1: A schematic landscape for eternally stable de Sitter space. The universe spends most of its time in the lowest minimum with rare fluctuations to higher points.
• Figure 2: Conformal diagram for 2-D de Sitter space and the static patch defined by a past and future pair of asymptotic points. The static patch (yellow) is the intersection of the causal future of the past point and the causal past of the future point. The intersection of the two light cones shown as red dots defines the bifurcate horizon. The dashed blue curve indicates identification of the left and right edges.
• Figure 3: Two static patches in the same dS.
• Figure 4: Upper panel: Penrose diagram for higher dimensional de Sitter space. Static patches come in pairs and the center of these patches are referred to as the pode and the antipode. Lower panel: the geometry of the $t=0$ slice of de Sitter space is a sphere with the pode at one pole and the antipode at the other. The dashed surface midway between the pode and antipode is the bifurcate horizon.
• Figure 5: Penrose diagrams supplemented with Bousso wedges for the AdS eternal black hole and for de Sitter space .